Generalized chi-squared detector for LTI systems with non-Gaussian noise

TL;DR

This paper extends the tuning of chi-squared anomaly detectors to non-Gaussian noises in LTI systems by using Gaussian Mixture Models, enabling precise false alarm rate control with arbitrary noise distributions.

Contribution

It introduces a generalized approach for tuning chi-squared detectors for non-Gaussian noise using Gaussian Mixture Models, enhancing detection accuracy.

Findings

Effective detector tuning for non-Gaussian noise distributions.

Analytic tractability maintained through Gaussian Mixture Models.

Interpretation of the detector as multiple chi-squared detectors.

Abstract

Previously, we derived exact relationships between the properties of a linear time-invariant control system and properties of an anomaly detector that quantified the impact an attacker can have on the system if that attacker aims to remain stealthy to the detector. A necessary first step in this process is to be able to precisely tune the detector to a desired level of performance (false alarm rate) under normal operation, typically through the selection of a threshold parameter. To-date efforts have only considered Gaussian noises. Here we generalize the approach to tune a chi-squared anomaly detector for noises with non-Gaussian distributions. Our method leverages a Gaussian Mixture Model to represent the arbitrary noise distributions, which preserves analytic tractability and provides an informative interpretation in terms of a collection of chi-squared detectors and multiple Gaussian disturbances.